Referring to FIGS. 8 to 10, a conventional tool assembly for screwdriver with detachable drill bits has a connecting rod (70), a sliding sleeve (80) and a C-shaped fastener (90). The connecting rod (70) comprises a circular shaft (71), and a first end thereof has a hexagonal connecting portion (72). An annular groove (73) formed on a surface of the connecting portion (72) is configured to connect with an electric tool or a pneumatic tool. An outer periphery of a second end of the shaft (71) has four cutting surfaces (74) to form a connecting end (75) with a rectangular cross section. Since an external diameter of connecting end (75) is smaller than the shaft (71), a flange (76) is formed at a connecting edge between the shaft (71) and the connecting end (75). Moreover, a locating ball (77) is mounted on an outer surface of the connecting end (75), and a magnetic unit (78) is secured at a front end thereof. A first peripheral groove (79) formed at an outer periphery of the shaft (71) is located adjacent to the flange (76). A circular connecting opening (81) and a tool slot (82) with a rectangular cross section are respectively and axially formed at a rear end and a front end of the sliding sleeve (80), and an inner blocking edge (83) is formed at a connecting edge between the connecting opening (81) and the tool slot (82). Also, a second peripheral groove (84) is formed at an inner periphery of the connecting opening (81), and each of inner edges of the tool slot (82) has a V-shaped groove (85). After the C-shaped fastener (90) is engaged with the first peripheral groove (79), the sliding sleeve (80) is connected to the shaft (71) through the connecting opening (81) such that the C-shaped fastener (90) is configured to engage with the first peripheral groove (79) and the second peripheral groove (84) simultaneously. Furthermore, since the inner blocking edge (83) and the flange (83) are configured to bear against each other so as to limit the sliding displacement of the sliding sleeve (80) on the connecting rod (70). In actual application, by pushing the sliding sleeve (80) rearward, the connecting end (75) is configured to protrude from a front end of the tool slot (82) thereby connecting a tool socket (as shown in FIG. 11). Meanwhile, since the inner blocking edge (83) is borne against the flange (76) when the sliding sleeve (80) moved rearward thus stopping the displacement of the sliding sleeve (80). Otherwise, when the sliding sleeve (80) is moved forward (as shown in FIG. 12), the connecting end (75) is completely received inside the tool slot (82) such that the tool slot (82) is configured to has a housing space to receive a tool head and the V-shaped grooves (85) are configured to engage with each outer edges of the tool head. As a result, the connecting rod (70) is configured to drive and rotate the tool head. Also, when the sliding sleeve (80) is moved forward, the C-shaped fastener (90) is configured to engage with the first peripheral groove (79) and the second peripheral groove (84) simultaneously thus limiting the maximum displacement of the sliding sleeve (80).
However, the conventional tool assembly for screwdriver with detachable drill bits is disadvantageous because: the application thereof is limited by the use of the C-shaped fastener (90) and positions of the first peripheral groove (79) and the second peripheral groove (84), the sliding sleeve (80) and the connecting end (75) need to be elongated to adjust a sliding distance of the sliding sleeve (80) on the connecting rod (70) which increases the manufacturing cost and further reduces the competitive advantage in the market. Therefore, there remains a need for a new and improved design for a tool assembly for screwdriver with detachable drill bits to overcome the problems presented above.